Phase-field models have various applications in diverse regions such as hydrodynamics, material sciences, image processing and biology simulation, etc.
Most phase-fields models are derived as gradient flows associating with some specific energy functional, such as the Ginzburg–Landau energy for Allen–Cahn equations and Cahn–Hilliard equations, Swift–Hohenberg energy for phase-field crystal models.
Seeking numerical solutions of phase-field equations has attracted a lot of attentions in the passed decade, which could be a delicate task: intrinsic properties of the solution shall be recovered on the discrete level (energy dissipation, maximum principle)
and the presence of small parameter \(\varepsilon > 0\)  can generate practical difficulties.
There have been plenty of numerical schemes for phase-field equations, including the convex-splitting schemes [1]}, [2]}, [3]}, [4]}, the stabilization schemes [5]}, [6]}, [7]}, the implicit-explicit (IMEX) schemes [8]}, [9]}, [10]}, the operator splitting methods [11]}, [12]}, the scalar auxiliary variable (SAV) schemes [13]}, [14]}, and the exponential time differencing (ETD) schemes [15]}, [16]}.
